Chaos and shadowing around a homoclinic tube
Let F be a C3 diffeomorphism on a Banach space B. F has a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. This work removes an uncheckable condition of Silnikov (1968). Also, the resul...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503304038 |
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| _version_ | 1832566588869443584 |
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| author | Yanguang (Charles) Li |
| author_facet | Yanguang (Charles) Li |
| author_sort | Yanguang (Charles) Li |
| collection | DOAJ |
| description | Let F be a C3 diffeomorphism on a Banach space B. F has a homoclinic tube asymptotic to an invariant manifold. Around the
homoclinic tube, Bernoulli shift dynamics of submanifolds is
established through a shadowing lemma. This work removes an
uncheckable condition of Silnikov (1968). Also, the result of Silnikov does not imply
Bernoulli shift dynamics of a single map, but rather only provides a
labeling of all invariant tubes around the homoclinic tube. The
work of Silnikov was done in ℝn and the current work is done in a Banach space. |
| format | Article |
| id | doaj-art-ff264431ccd74ad48a2736438cfd7c55 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ff264431ccd74ad48a2736438cfd7c552025-02-03T01:03:46ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-0120031692393110.1155/S1085337503304038Chaos and shadowing around a homoclinic tubeYanguang (Charles) Li0Department of Mathematics, University of Missouri, Columbia 65211, MO, USALet F be a C3 diffeomorphism on a Banach space B. F has a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. This work removes an uncheckable condition of Silnikov (1968). Also, the result of Silnikov does not imply Bernoulli shift dynamics of a single map, but rather only provides a labeling of all invariant tubes around the homoclinic tube. The work of Silnikov was done in ℝn and the current work is done in a Banach space.http://dx.doi.org/10.1155/S1085337503304038 |
| spellingShingle | Yanguang (Charles) Li Chaos and shadowing around a homoclinic tube Abstract and Applied Analysis |
| title | Chaos and shadowing around a homoclinic tube |
| title_full | Chaos and shadowing around a homoclinic tube |
| title_fullStr | Chaos and shadowing around a homoclinic tube |
| title_full_unstemmed | Chaos and shadowing around a homoclinic tube |
| title_short | Chaos and shadowing around a homoclinic tube |
| title_sort | chaos and shadowing around a homoclinic tube |
| url | http://dx.doi.org/10.1155/S1085337503304038 |
| work_keys_str_mv | AT yanguangcharlesli chaosandshadowingaroundahomoclinictube |